Device and method for measuring angles

ABSTRACT

A device for angle measurement, having at least one transducer wheel and at least one sensor, including at least one sensor element and cooperating with the transducer wheel, in which by means of the cooperation of the transducer wheel and the sensor, a pair, which can be associated with an angle to be measured, comprising one sine-wave signal and one cosine-wave signal can be obtained, in which at least two sensors are provided, whose sine-wave signals and cosine-wave signals, for obtaining an averaged sine-wave signal and averaged cosine-wave signal, and/or after the formation of an arc tangent signal from the respective averaged or unaveraged sine-wave signals or cosine-wave signals, can be put computationally into relation with one another by means of an evaluation device in order to obtain an averaged arc tangent signal.

BACKGROUND OF THE INVENTION

The present invention relates to a device for angle measurement and to acorresponding method.

The demand for high-precision yet also robust angle measuring systems inthe automobile industry is constantly rising. At present, the areas inwhich angle measuring systems are used include an electronic stabilityprogram (ESP) and electrically assisted steering systems. Over the longterm, the transition to steer-by-wire will increase the demand for anglemeasuring systems still further, and this development involves asimultaneous increase in the accuracy demanded.

Magnetic sensors are predestined for use in the automobile, because oftheir contactless, robust measurement principle. If an angle measuringsystem realized with magnetic sensors is based on scanning a transducerwheel that is either itself magnetized or comprising ferromagneticmaterial and on moving past the scanning sensor distorts the field of atransducer magnet, production tolerances limit the accuracy of thesystem. Aspects that are especially problematic are eccentricities,polarization or tooth pitch errors, and nonhomogeneities in the fieldamplitudes. Moreover, the scanning sensors cannot be positionedarbitrarily accurately, so that additional positioning tolerances arealso involved.

Conventional methods for angle measurement are known for instance fromGerman Patent Disclosure DE-P 195 34 995. German Patent Disclosure DE-P199 58 598.9, which had not yet been published by the filing date of thepresent application, for instance describes a Nonius method, in whichmagnetic multipole wheels, each with a different number of pole pairs,are used, and the sensor signals obtained from suitably disposed sensorsare evaluated. Once again, however, angle errors are caused by theaforementioned tolerances.

SUMMARY OF THE INVENTION

It is therefore the object of the invention to disclose a device and amethod for angle measurement in which angle errors caused by tolerancesare reduced.

By the provision according to the invention of a number of sensors, andthe averaging of the signals obtained, based on the individual sensorsignals, the effects of the aforementioned tolerances on the measurementaccuracy can be reduced in a highly effective way.

In a preferred embodiment of the device of the invention, three sensorsare provided, which are distributed about the at least one transducerwheel. Sensors arranged at 120° angles from one another form an idealcompromise between the lowest possible number of sensors and thefunctional capability of the device. Moreover, there are advantages fromsymmetry in terms of production tolerances. However, it should beemphasized that the method of the invention also functionssatisfactorily when only two sensors are used. To further increase theaccuracy, however, more than two sensors can also be used.

Expediently, two transducer wheels that are rotatable about a commonpivot axis and are disposed in a manner fixed against relative rotationwith respect to one another are provided, and the transducer wheels havea different number of transducer segments. According to the invention,arbitrary transducer wheels that utilize magnetic or nonmagneticmeasurement principles can be used. For instance, in the case ofmagnetic multipole wheels, the transducer segments are embodied as polepairs, while in the case of ferromagnetic gear wheels, they are embodiedas teeth.

In this respect it is advantageous that the first transducer wheel has nsegments, and the second transducer wheel has n+1 segments. Forinstance, n can equal 24, but other values can also be selected,depending on the accuracy to be required. Such an embodiment with twodifferent transducer wheels makes it possible to use so-called Noniusmethods, with which especially reliable evaluation of the sensor signalsobtained is possible.

Expediently, the sensors are embodied as Hall sensors. Such Hall sensorscan be obtained economically and prove to be robust and reliable inpractice.

In a further preferred feature of the device of the invention, the atleast one transducer wheel is embodied as a magnetic multipole wheel.

In an especially preferred feature of the method of the invention, aharmonic correction is performed before and/or after the averaging ofthe sine-wave signals or cosine-wave signals or arc tangent signalsobtained. This kind of harmonic correction can for instance be performedon the basis of a series development, such as Fourier series developmentof the sine-wave signals or cosine-wave signals obtained.

It is also preferred that the arc tangent averaging includes an offsetcorrection and/or a modulo division for adapting the phase and valuesrange of the various arc tangent signals to be averaged and/or theformation of the arithmetic mean from the thus-modified arc tangentsignals.

Expediently, the formation of the arithmetic mean is effected bycomputationally taking into account the discontinuities of the arctangent signals to be averaged.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will now be described in further detail in conjunctionwith the accompanying drawing. Shown in it are

FIG. 1, a graph explaining an angle measurement that can be done withthe device;

FIGS. 2 a–2 c, graphs for explaining an error reduction, which can beachieved with the method of the invention, in the angle measurement;

FIGS. 3 a and 3 b schematic plan views of a first preferred embodimentof the device of the invention;

FIG. 4, a graph showing a Fourier synthesis of a square wave function;

FIG. 5, a graph showing angle errors in sine and cosine averaging andwith an offset of 0.25 mm between two sensors or sensor elements;

FIGS. 6 a–6 d, graphs showing the computational processing of a sensoroffset by phase adaptation and ensuing arc tangent averaging; and

FIG. 7, a graph showing the angle error for the case of an extremeoffset between two sensors or sensor elements of 1 mm each after an arctangent averaging and additionally with a prior harmonic correction.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The drawing description below pertains to the special embodiment ofscanning of a magnetic multipole wheel. However, the method can also beattained advantageously with other transducer wheels involvingnonmagnetic or magnetic measuring principles. The measured values andmeasurement errors indicated below refer by way of example to polewheels with n=12 and n=13 pole pairs, and with an outer diameter of 30.8mm.

The measurement principle on which the invention is based will first beexplained in conjunction with FIG. 1.

A steering column is embodied with a torsion bar. Concentrically to thetorsion bar, three magnetic multipole wheels are provided. Upon arotation of the upper part of the steering column relative to the lowerpart about its longitudinal axis, an angular displacement of themagnetic multipole wheel 13 a occurs relative to the remaining magneticmultipole wheels. Disposed next to the multipole wheels is a sensor 12,which has three sensor elements 12 a, 12 b, 12 c that are associatedwith the multipole wheels 13 a, 13 b and 13 c, respectively. Because ofthe interaction between the individual multi pole wheels and the sensorelements associated with them, trigonometric signals are generated, fromwhich the angular position of the torsion bar can be derived. Here, ameasured angular position relative to the magnetic multipole wheel 13 aserves as a reference for the angular position that is ascertained bymeans of the other magnetic multipole wheels 13 b and 13 c, as will nowbe explained in conjunction with FIG. 21. In FIG. 21, the signalsproduced upon a rotation of the multipole wheels 13 b, 13 c past therespective sensor elements 12 b and 12 c are shown.

The sensor elements 12 b, 12 c each detect one sine-wave signal (solidlines) and one cosine-wave signal (dashed lines). By finding the arctangent of the respective pairs of signals, two arc tangent signalsα(φ), β(φ) are obtained, which in accordance with the differentperiodicity of the respective sine/cosine signal pairs, because of thedifferent number of pole pairs, also have a different periodicity. Bythe classical Nonius method, a function φ=α(φ)−β(φ) is now generated,which unequivocally describes the rotational angle φover the entireangular range of 360°.

The cosine-wave signals and sine-ways signals of sensor elementsdisposed in this way are, however, dependent on positioning andproduction tolerances. This will first be illustrated in conjunctionwith FIG 2. FIG. 2 a, top, shows the magnetic field, measured with aHall sensor (such as sensor element 12 bor 12 c), of a typical multipolewheel as a function of the angle; this multipole wheel has already beenoptimized for pitch and amplitude errors. Together with a signal phaseoffset from it, which is furnished either by the same or by anadditional sensor element, a rotational angle and a position above apole pair can be determined, as already described in conjunction withFIG. 1. However, an error in the position determination is transferredto the rotational angle of the pole wheel and thus to the entire sensorsystem.

Although the sine-wave sensor signal shown at the top of FIG. 2 aalready originates in a transducer wheel that has been optimized forpitch and amplitude errors, an eccentricity in the form of an envelopecan nevertheless be seen. This eccentricity is expressed as an angleerror, which in the worst case (at angles of approximately 100°), is±0.4°. The second major error source can also already be seen in theform of higher-frequency modulation. The transducer field of magneticmultipole wheels in fact has a square-wave portion that increases as thespacing between the sensor and the pole wheel decreases and that isexpressed in the periodic deviation from the ideal sine-wave transducerfield (in this respect also see FIG. 4).

To eliminate the effects of an eccentricity of the transducer wheelrelative to its pivot axis, it is now proposed according to theinvention that a plurality of sensors or sensor elements be disposedaround the transducer wheel, and that the arithmetic mean of theindividual sensor signals be formed. In FIG. 3 a three sensors 121, 122,123 are seen, which are disposed concentrically about a multipole wheel23 at 12O° angles from one another. A further multipole wheel 24 is alsoshown in FIG. 3 b, with which the sensors 124, 125, 126 am associated.The multipole wheel 24 differs from the multipole wheel 23 in having adifferent number of multipoles. The multipole wheels 23, 24 are shownnext to each other solely to make the different numbers of multipolesmore readily apparent. It is assumed that they are disposed coaxiallyone above the other. It will be noted that each sensor 121, 122, 123,124, 125,126 here can have a plurality of sensor elements, whichgenerate sine-wave signals and cosine-wave signals that are in a fixedphase relationship to one another. The signals obtained from the varioussensors can be delivered to an evaluation device 20.

Expediently, In a first preferred embodiment of the method of theinvention, the three sine-wave signals obtained for each transducerwheel and the three cosine-wave signals are now averaged arithmetically;on the basis of these averaged sine-wave signals and cosine-wavesignals, a corresponding arc tangent signal is generated. Thedescription that follows relates to the signals that can be obtainedwith a single transducer wheel. Combining the signals of two or moretransducer wheels, as has been described above with reference to FIG. 1,is understood to be possible as an additional provision. In the eventthat for one transducer wheel three arc tangent signals ascertained inthis way are averaged, the error shown in FIG. 2 b, middle, of ±0.4° isreduced to ±0.4°, as shown in FIG. 2 c bottom, curve A. The originalangle error resulting from the raw data with the arc tangent method canthus be reduced by a factor of 10.

It should also be noted that the shorter the distance between a sensorand the multipole wheel, the greater the deviation of a generated sensorsignal is from the sine-wave to a square-wave function. This square-wavefunction can be represented, as shown in FIG. 4, in the form of aFourier series: a ₁ sin(cx)+a₃ sin(3cx)+a₅ sin(5cx)+ . . . . Theparameter c is fixedly predetermined by the number of poles. The Fouriercoefficients a that is, the harmonics, can easily be determined byadaptation of the measurement signal. Even only one to two harmonics aresufficient to reduce the error to ±0.2° as shown in FIG. 2 c, bottom,curve B. Moreover, with this method, if magnetoresistive sensors areused, problematic anisotropic effects can be compensated for.

In the description above, it has been assumed that the sensors can bedisposed quite precisely and in a well controlled way around therespective transducer wheels. Under real conditions, however, productiontolerances have to be considered. Such production tolerances can forinstance be due to the fact that a sensor element may not be centrallyplaced in its housing. Although in such a case the harmonic reductiondescribed still functions, nevertheless the averaging function isdrastically worse, as shown in FIG. 5. It is shown here that for anoffset of the sensors by 0.25 mm, an angle error of ±0.15° alreadyresults. The main reason for this effect is that the various sensors,such as the sensors 121, 122, 123 shown in FIG. 3 no longer measure thesame phase of the transducer field. To compensate for such effects, afurther preferred embodiment of the method of the invention will now bedescribed, in conjunction with FIGS. 6 a–6 d, which can be usedalternatively or in addition to the procedures already described. Here,it is assumed that first for each individual sensor, such as the sensors121, 122, 123 of FIG. 2 a one arc tangent signal is generated from thevarious sine-wave signals and cosine-wave signals obtained. However,because of the offset of the sensors, they have an arbitrary phase, asshown in FIG. 6 a. To adapt the phase for later averaging, first theoffset of the arc tangent is subtracted, as shown in FIG. 6 b. Next, amodulo division is performed; that is, the function regions that arenegative because of the subtraction of the offset are appended, as shownin FIG. 6 c, to the respective peaks of the arc tangent function (thatis, the value of 1 is added to the negative function values). Theresultant signal, which is shown in part as a dotted line and in part asa solid line in FIG. 6 c, has a phase and a values range that match oneother. With the modified am tangent signal obtained for each of thethree sensors 121, 122, 123 an averaging is now performed.

In this averaging, which is shown schematically for two arc tangentsignals in 6 d the arithmetic mean of the modified arc tangent signalsis formed. It is assumed here that the arc tangent functions α₁ and α₂are to be averaged. In particular, the discontinuities should be takeninto account, which occur at the beginning (function α₁) and at the end(function α₂) of the Interval X. Simple addition of the function valuesin this interval would produce unsatisfactory results, since adding thefunction values at point X₁, for instance, would lead to an averagedfunction value that is below the function value of α₂. One possible wayof avoiding this difficulty is to add 1 to the lower measurement values,in the regions where measurement values are in the upper and lowerquarter of the values range, that is, in the interval X, and only afterthat to form the arithmetic mean. Expediently, a modulo division is thenagain performed, so that the measured values are again at the correctinterval [0;1]. Alternatively, the standard deviation could be looked atin order to detect a discontinuity.

Analogously to the averaging described above for eliminating theeccentricity, it is also possible in each of the arc tangent averagingmethods described to perform the harmonic correction, also alreadydescribed —as a first step, separately for each sensor element. If anextreme offset of 1 mm for each of the sensor elements is assumed, thenwith this method an accuracy of 0.04° is still obtained, as shown inFIG. 7, curve C. Without a harmonic correction, an angle error curvewith an error of 0.06° is obtained, as shown in FIG. 7 by curve D.

Overall, an arc tangent signal is obtained that corresponds for instanceto the signal α(φ) of FIG. 1 which however compared to that signal issubstantially less vulnerable to error or has substantially less error.After a second arc tangent signal corresponding to the signal β(φ) isanalogously obtained, the described Nonius method can for instance beemployed.

1. A method for angle measurement on the basis of at least one pair of signals, to be associated with an angle to be measured, comprising one sine-wave signal and one cosine-wave signal, which are generated by interaction of transducer wheel means with sensor means: wherein the transducer wheel means comprises two transducer wheels that are rotatable about a common pivot axis and are disposed in a manner fixed against relative rotation with respect to one another with the transducer wheels having a different number of transducer poles, wherein the sensor means comprises three sensors distributed around each transducer wheel which provide at least two pairs of signals each comprising one sine-wave signal and one cosine-wave signal, and the sine-wave signals and cosine-wave signals of the at least two pairs of signals for obtaining an averaged sine-wave signal and an averaged cosine-wave signal, and after the formation of an arc tangent signal from the averaged or unaveraged sine-wave signals and cosine-wave signals, are put computationally into relation with one another for obtaining an averaged arc tangent signal, wherein a harmonic correction of signals obtained is performed before and/or after averaging of these signals, wherein two output signals of the sensors are developed in Fourier series and Fourier coefficients which correspond to harmonics are determined and taken into consideration during a signal processing.
 2. A method for angle measurement on the basis of at least one pair of signals, to be associated with an angle to be measured, comprising one sine-wave signal and one cosine-wave signal, which are generated by interaction of transducer wheel means with sensor means; wherein the transducer wheel means comprises two transducer wheels that are rotatable about a common pivot axis and are disposed in a manner fixed against relative rotation with respect to one another with the transducer wheels having a different number of transducer poles, wherein the sensor means comprises three sensors distributed around each transducer wheel which provide at least two pairs of signals each comprising one sine-wave signal and one cosine-wave signal, and the sine-wave signals and cosine-wave signals of the at least two pairs of signals for obtaining an averaged sine-wave signal and an average cosine-wave signal, and after the formation of an arc tangent signal from the averaged or unaveraged sine-wave signals and cosine-wave signals, are put computationally into relation with one another for obtaining an averaged arc tangent signal, wherein arc tangent averaging includes an offset correction and a module division for adapting phase and values range of various arc tangent signals to be averaged and a formation of an arithmetic mean from averaged arc tangent signals.
 3. The method of claim 2, wherein the formation of the arithmetic mean is effected by computationally taking into account discontinuities of the arc tangent signals to be averaged.
 4. The method of claim 2, wherein a harmonic correction of signals obtained is performed before and/or after the averaging of these signals, wherein two output signals of the sensors are developed in Fourier series and Fourier coefficients which correspond to harmonics are determined and taken into consideration during a signal processing.
 5. A device for angle measurement, having transducer wheel means and sensor means cooperating with me transducer wheel means, in which by cooperation of the transducer wheel means and the sensor means, a pair of signals, which can be associated with an angle to be measured, comprising one sine-wave signal and one cosine-wave signal are obtained. wherein the transducer wheel means include two transducer wheels that are rotatable about a common pivot axis and are disposed in a manner fixed against relative rotation with respect to one another, and the transducer wheels have a different number of transducer poles. wherein the sensor means include three sensors distributed around each transducer wheel, whose sine-wave signals and cosine-wave signals, for obtaining an averaged sine-wave signal and an averaged cosine-wave signal, and after the formation of an arc tangent signal from the averaged or unaveraged sine-wave signals and cosine-wave signals, are put computationally into relation with one another for obtaining an averaged arc tangent signal, wherein a harmonic correction of signals obtained is performed before and/or after averaging of those signals, wherein two output signals of the sensors are developed in Fourier series and Fourier coefficients which correspond to harmonics are determined and taken into consideration during a signal processing.
 6. The device of claim 5, wherein the first transducer wheel has n poles pairs, and the second transducer wheel has n+1 poles pairs.
 7. The device of claim 5, wherein the sensors are embodied as Hall sensors.
 8. The device of claim 5, wherein the transducer wheels are embodied a magnetic multipole wheels.
 9. A device for angle measurement, having transducer wheel means and censor means cooperating with the transducer wheel means, in which by cooperation of the transducer wheel means and the sensor means, a pair of signals, which can be associated with an angle to be measured, comprising one sine-wave signal and one cosine-wave signal are obtained, wherein the transducer wheel means include two transducer wheels that are rotatable about a common pivot axis and are disposed in a manner fixed against relative rotation with respect to one another, and the transducer wheels have a different number of transducer poles, wherein the sensor means include three sensors distributed around each transducer wheel, whose sine-wave signals and cosine-wave signals, for obtaining an averaged sine-wave signal and an averaged cosine-wave signal, and after the formation of an arc tangent signal from the respective averaged or unaveraged sine-wave signals and, cosine-wave signals, are put computationally into relation with one another for obtaining an averaged arc tangent signal, wherein arc tangent averaging includes an offset correction and a modulo division for adapting phase and values range of various arc tangent signals to be averaged and a formation of an arithmetic mean from averaged arc tangent signals.
 10. The method of claim 9, wherein a harmonic correction of signals obtained is performed before and/or after averaging of these signals, wherein two output signals of the sensors are developed in Fourier series and Fourier coefficients which correspond to harmonics are determined and taken into consideration during a signal processing. 